Sampling from Boltzmann densities with physics informed low-rank formats

TL;DR

This paper introduces a novel method for efficiently sampling from unnormalized Boltzmann densities using a low-rank tensor train format, combining deterministic flow steps with stochastic resampling inspired by Sequential Monte Carlo.

Contribution

The paper presents a new approach that integrates low-rank tensor train representations with annealing-based sampling, enhancing efficiency over traditional methods.

Findings

Effective sampling demonstrated on multiple numerical examples.

Combines deterministic flow with stochastic resampling for improved performance.

Reduces computational complexity in sampling from Boltzmann densities.

Abstract

Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.